منابع مشابه
Imaginary Powers of Laplace Operators
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Let ∆ be an arbitrary linear differential operator of the second order acting on functions on a (super)manifold M . In local coordinates ∆ = 1 2 S ∂b∂a +T a ∂a +R. The principal symbol of ∆ is the symmetric tensor field S, or the quadratic function S = 1 2 Spbpa on T ∗M . The principal symbol can be understood as a symmetric “bracket” on functions: {f, g} := ∆(fg) − (∆f) g − (−1)f (∆g) + ∆(1) f...
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The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05754-3